craftgrrl | Sewing machine help!

I got a used Singer 247 sewing machine a few weeks ago and took it to the shop to get all fixed up. They charged me 60 dollars and it worked great for a couple weeks. Tonight it just stopped working, and the wheels underneath would no longer turn with the hand knob or while the machine was running. After several hours of inspecting, I finally traced it up to this gear on the inside - it is supposed to turn with the hand knob gear in order to run the wheels on the bottom of the machine. But upon opening up the machine, I found that everything was really grimy/dirty in there and the gear in question had completely eroded away... all of its teeth have just withered away so that it can no longer connect with the adjacent gear, and the wheels on the bottom of the machine cannot turn.

So I am really angry that the shop didn't recognize this when they supposedly did a complete renovation of the thing... and will probably want to charge me even more money to fix this now. I am just wondering - is it feasible to try and find a replacement and install it on my own, or should I go back to the shop and demand an inexpensive fix? It just seems like they didn't even LOOK on the inside of the machine because it was so dirty and corroded - when the receipt they gave me said that they completely cleaned and tuned it up. Any advice on this, and would it be possible for me to replace the part myself?

Here's a picture to show you where the part is - it's hard to see the erosion of the teeth, but it's there. The gear seems buried under so many other parts that I'd probably have to dismantle the whole thing to get to it.